Find the future value if $2000 is invested for 10 years at 13% compounded annually. (Round your answer to the nearest cent.)
$ 
 

The formula to calculate the future value $ A $ of an investment compounded annually is:

\[
A = P(1 + r/n)^{nt}
\]

Where:
- $ A $ = future value of the investment
- $ P $ = initial investment (principal) = $2000
- $ r $ = annual interest rate = 13% = 0.13
- $ n $ = number of times the interest is compounded per year (for annual compounding, $ n = 1 $)
- $ t $ = time the money is invested for = 10 years

Substituting the given values:

\[
A = 2000(1 + 0.13/1)^{1 \times 10} = 2000(1.13)^{10}
\]

Calculating:

\[
A = 2000 \times (1.13)^{10} \approx 2000 \times 3.3934 \approx 6786.84
\]

So, the future value is approximately **$6786.84**.

Would you like further details or have any questions?

Here are some related questions:
1. How would the result change if the interest was compounded quarterly?
2. What if the interest rate was 10% instead of 13%?
3. How do we calculate the future value if compounding is continuous?
4. How does the investment period affect the future value?
5. What if you added more money periodically to the investment?

**Tip:** The more frequently interest is compounded, the greater the future value due to the effect of compound interest!

Find the future value if $2000 is invested for 10 years at 13% compounded annually. (Round your answer to the nearest cent.)

Learn how to calculate the future value of a $2000 investment over 10 years at 13% annual interest compounded once per year. The solution involves applying the compound interest formula and exponentiation to find the future value, which is approximately $6786.84. This problem is suitable for high school students (Grades 9-12).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation